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In ΔABC, D is a point on BC such that ∠ADB = 2∠DAC, ∠BAC = 70° and ∠B = 56°. What is the measure of ∠ADC?

In ΔABC, D is a point on BC such that ∠ADB = 2∠DAC, ∠BAC = 70° and ∠B = 56°. What is the measure of ∠ADC? Correct Answer 72°

Given:

In ΔABC, D is a point on BC 

∠ADB = 2∠DAC

∠BAC = 70° and ∠B = 56°

Concept Used:

linear pair of angles 

Sum of linear pair of angles = 180° 

Sum of angles of triangle = 180° 

Calculation:

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Let ∠BAC = x° 

So, ∠ADB = 2x° 

Since, ∠BAC = 70° 

So, ∠BAD = (70 - x°)

Now, In ΔABD 

56° + 2x° + 70 - x° = 180° 

⇒ x = 54° 

⇒ 2x = 108° 

Now, By linear pair of angles 

∠ADB + ∠ADC = 180° 

⇒ 2x + ∠ADC = 180° 

⇒ 108° + ∠ADC = 180° 

⇒ ∠ADC = 180° - 108°

⇒ ∠ADC = 72° 

∴ The required measurement of angle is 72°.

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